Overview
- Proof complexity is a research area that studies the concept of complexity from the point of view of logic
- Book offers a reader-friendly exposition of game-theoretic methods used in proof complexity
- Appropriate for researchers in theoretical computer science, in particular computational complexity
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Table of contents (8 chapters)
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Front Matter
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General Results and Techniques
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Front Matter
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Applications
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Front Matter
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A Postlude
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Front Matter
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Back Matter
Keywords
About this book
This book considers logical proof systems from the point of view of their space complexity. After an introduction to propositional proof complexity the author structures the book into three main parts. Part I contains two chapters on resolution, one containing results already known in the literature before this work and one focused on space in resolution, and the author then moves on to polynomial calculus and its space complexity with a focus on the combinatorial technique to prove monomial space lower bounds. The first chapter in Part II addresses the proof complexity and space complexity of the pigeon principles. Then there is an interlude on a new type of game, defined on bipartite graphs, essentially independent from the rest of the book, collecting some results on graph theory. Finally Part III analyzes the size of resolution proofs in connection with the Strong Exponential Time Hypothesis (SETH) in complexity theory.
The book is appropriate for researchers in theoretical computer science, in particular computational complexity.
Authors and Affiliations
About the author
Ilario Bonacina did his PhD at the Computer Science Department at Sapienza Università di Roma under the supervision of Nicola Galesi. After a postdoc in the Theoretical Computer Science Group at KTH Royal Institute of Technology (Stockholm), he is currently a postdoc in the Computer Science Department at Universitat Politècnica de Catalunya (Barcelona). His research interests include computational complexity and mathematical logic.
Bibliographic Information
Book Title: Space in Weak Propositional Proof Systems
Authors: Ilario Bonacina
DOI: https://doi.org/10.1007/978-3-319-73453-8
Publisher: Springer Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-73452-1Published: 24 January 2018
Softcover ISBN: 978-3-319-89249-8Published: 07 June 2019
eBook ISBN: 978-3-319-73453-8Published: 11 January 2018
Edition Number: 1
Number of Pages: XVII, 130
Number of Illustrations: 7 b/w illustrations, 8 illustrations in colour